I've considered doing this for some time now. Do you have any sort of link between the two accounts? Maybe not directly, but e.g. are both connected to the same brokerage or anything? Is one online-only or do both have physical locations somewhere?

One is online only (the one I use the most), the other one is a completely different bank with very different objectives and clients plus physical offices everywhere.

Each account can send money to the other via wiring, but that's it.

Saved my ass several times already when I lost my credit cards or other unpleasant situations.

When something similar happened with an immigrant co-worker in the UK, I quickly picked up a second bank account.

He got stuck for about a week and a half with his money all locked up in an account he couldn't access. It was early enough in the month that rent and bills etc. wasn't an issue, we just ended up helping him out buying food for a few days while he sorted out another account and got an advance on his salary.

I remember the range of excuses and explanations for delays from the bank left us all gobsmacked.